Optimal lrcs - Open Access .click

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Long Optimal and Small-Defect LRC Codes With Unbounded Minimum Distances

IEEE Transactions on Information Theory, 2021
For a linear locally recoverable (LRC) code with length $n$ , dimension $k$ and locality $r$ , its minimum distance $d$ satisfies ${d} \leq {n}-{k}+2-\lceil \frac {{k}}{{r}}\rceil $ . A code attaining this bound is called optimal.
Hao Chen 0029 +3 more
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On the Maximal Code Length of Optimal Linear LRC Codes with Availability

2018 Engineering and Telecommunication (EnT-MIPT), 2018
A code over finite alphabet is said to be locally recoverable (LRC) if each code symbol is function of small number of other symbols forming the recovering set [1], [2], [3], [4], [5]. These codes were first proposed in [1] and immediate become popular due to obvious applications in distributed and cloud storage systems.
Stanislav Kruglik, Kamilla Nazirkhanova, Alexey Frolov +2 more
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Optimal LRC codes for all lenghts n <= q

2018
A family of distance-optimal LRC codes from certain subcodes of $q$-ary Reed-Solomon codes, proposed by I.~Tamo and A.~Barg in 2014, assumes that the code length $n$ is a multiple of $r+1.$ By shortening codes from this family, we show that it is possible to lift this assumption, still obtaining distance-optimal codes.
Kolosov, Oleg +3 more
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Some Properties and Constructions of Weakly Self Dual LRCs

2022
Satya Bagchi
exaly

A characterization of optimal locally repairable codes

Discrete Mathematics, 2023
Fagang Li, Shanxiang Lyu
exaly

Singleton-optimal (r, δ)-LRCs via some good polynomials of special forms.

CoRR, 2022
Yuan Gao, Siman Yang
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Optimal (r, δ)-LRCs from zero-dimensional affine variety codes and their subfield-subcodes.